The desire to understand normal and disordered human brain function of upright, moving persons in natural environments motivates the development of the ambulatory micro-dose brain PET imager (AMPET). An ideal system would be light weight but with high sensitivity and spatial resolution, although these requirements are often in conflict with each other. One potential approach to meet the design goals is a compact brain-only imaging device with a head-sized aperture. However, a compact geometry increases parallax error in peripheral lines of response, which increases bias and variance in region of interest (ROI) quantification. Therefore, we performed simulation studies to search for the optimal system configuration and to evaluate the potential improvement in quantification performance over existing scanners. We used the Cramér-Rao variance bound to compare the performance for ROI quantification using different scanner geometries. The results show that while a smaller ring diameter can increase photon detection sensitivity and hence reduce the variance at the center of the field of view, it can also result in higher variance in peripheral regions when the length of detector crystal is 15 mm or more. This variance can be substantially reduced by adding depth-of-interaction (DOI) measurement capability to the detector modules. Our simulation study also shows that the relative performance depends on the size of the ROI, and a large ROI favors a compact geometry even without DOI information. Based on these results, we propose a compact 'helmet' design using detectors with DOI capability. Monte Carlo simulations show the helmet design can achieve four-fold higher sensitivity and resolve smaller features than existing cylindrical brain PET scanners. The simulations also suggest that improving TOF timing resolution from 400 ps to 200 ps also results in noticeable improvement in image quality, indicating better timing resolution is desirable for brain imaging.